Distribution Modulo One of αpγ + β for Special Classes of Primes - Atanaska Georgieva; Tatiana L. Todorova (Axioms)
Let <semantics>α,β∈R</semantics> with <semantics>α≠0</semantics>, and let <semantics>γ∈(0,5/6)</semantics>. Define the set <semantics>M1</semantics> to consist of primes p such that <semantics>p+2</semantics> is almost prime, and let <semantics>M2</semantics> be the set of primes of the form <semantics>p=a2+b2+1</semantics>. We study the distribution of <semantics>αpγ<mtext> </mtext>+<mtext> </mtext>β</semantics> modulo one, as p ranges over the sets <semantics>M1</semantics> and <semantics>M2</semantics>, respectively.